Problem: Reduce to lowest terms: $ \dfrac{5}{4} \div - \dfrac{1}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{1}{5}$ is $- \dfrac{5}{1}$ Therefore: $ \dfrac{5}{4} \div - \dfrac{1}{5} = \dfrac{5}{4} \times - \dfrac{5}{1} $ $ \phantom{ \dfrac{5}{4} \times - \dfrac{5}{1}} = \dfrac{5 \times -5}{4 \times 1} $ $ \phantom{ \dfrac{5}{4} \times - \dfrac{5}{1}} = \dfrac{-25}{4} $